Here are some solved problems dealing with the conservation of angular momentum for you to examine before trying some on your own. (*Note: The values in these problems are not at all realistic and are not meant to be taken in that way. They are simply made up to further your understanding of the topic.)
A planet is in and elliptical orbit around the sun. If the radius of the Apogee point of its orbit is 35000 km, and at another point on its path where the radius is 20000 km its orbital speed 200 km/hr.
The first step to solving this problem is to get all the values into SI units (meters, meters per second). After doing this, we can use the conservation of angular momentum formula:
m(v1)(r1) = m(v2)(r2)
Since the mass of the planet doesn't change, we can cancel that value from both sides so we really don't need to know it to solve this problem. Now lets plug in the values and solve.
(2.0 * 10^7 m)(55.6 m/s) = (3.5 * 10^7 m)(v2)
1.1 * 10^9 = (3.5 * 10 ^7)(v2)
31.7 m/s = v2
A skater spins with her arms extended at a speed of 11 m/s. If she then whips her arms in to her body to form a circle with a radius of 0.4 m and spins at a new speed of 24 m/s, what was the radius of the circle that she formed with her arms extended? (Assume net external torque is zero)
Since the net external torque acting on the system is zero, the laws of conservation of angular momentum can be applied here. This means we can use the formula and solve for the missing values. Again the m value doesn't change, so it can be excluded.
(v1)(r1) = (v2)(r2)
(11 m/s)(r1) = (24 m/s)(0.4 m)
r1 = 0.9 m
Now that you have seen some examples that have been solved for you, head over to the Conservation of Angular Momentum Problems Page and try some for yourself.
